Introduction to Mathematical Modelling
SPARK short course ‘Mathematical Modelling of Infectious Diseases’, Yogyakarta, Indonesia, 2023
Thanks to Lisa White, Nuffield Department of Medicine, Oxford University and
Wirichada Pan-Ngum, Department of Tropical Hygiene, Faculty of Tropical Medicine, Mahidol University.
Adapted and presented by Emma McBryde, Australian Institute of Tropical Health & Medicine, James Cook University
Summary
This is an interactive session to introduce the basic concepts of mathematical modelling of infectious diseases. The SIRS model will be derived and explained. Typical epidemiological measures such as prevalence, incidence and the basic reproduction number will be explored. Types of transmission dynamic models will be compared.
This session is divided into three parts:
Part 1 covers:
- Brief introduction to the module
- First practical session
Part 2 covers:
- Explanation of the dynamic relationships between the changing numbers of susceptible (S), infectious (I), and recovered (R) individuals
- Introduction to key definitions
- Introduction to compartmental modelling
Part 3 covers:
- Development of the running example model for the module which will be revisited in multiple subsequent sessions
- Review of selected biological information to derive an appropriate model structure
- Further review of the information will guide participants to extract essential parameter values
We recommend to save your text at the end of each part by printing the file.
Introduction
What is a model?
- A simplified description of a system or process used to aid understanding
- A model is useful if it provides relevant (and correct) information for a particular purpose/question
- A model is efficient if it will do this with minimal inputs and without providing superfluous information
- Map example: https://www.thetruesize.com/
Why use mathematical models?
Types of infectious disease model
Covered in this course:
- Mechanistic models
- Describe the biological mechanism in mathematical language
- Can reproduce previous trends and also predict future impacts of interventions
Not covered in this course:
- Economic models
- Focus on the cost specific disease burden and control
- Assess the cost-effectiveness of competing interventions
- Bioinformatics
- Mainly for the analysis and interpretation of genetic data
- Statistical models
- Data-driven and describe historical trends and relationships such as auto-regressive models
- Spatial models (though they will be discussed briefly)
- Focus on spatially heterogeneous systems
There are many examples of hybrid models that span several of these categories.
Model Complexity - or not!
- Models should be formulated based on understanding of disease mechanisms, available information and policy questions
- Models should be as simple as possible, but no simpler
- Some models are simple but useful
- The more functions a model performs, the more complex it becomes
- Faster processing speed, new methods and technology allow for more complexity
- but this is not always superior
Advice: start simple and build
Part 1: Our first model
Summary
This is a practical session in which, individually or as part of a group, you will simulate an epidemic using some simple apparatus. The objective of this exercise is to simulate and graphically illustrate the SIR compartmental model.
Materials
- Three types of beans of a similar size but different colours, 20 of each type
- An A4 piece of paper, folded in quarters in concertina style
- One cup